Compound interest calculator

How compound interest works

Compound interest is what happens when the interest you earn on an investment starts earning its own interest. It's the difference between simple growth (linear) and compounding growth (exponential). Albert Einstein reportedly called it "the eighth wonder of the world" — and the longer you give it, the more powerful it becomes.

The standard compound interest formula with regular contributions is:

FV = P × (1 + r)ⁿ + PMT × [((1 + r)ⁿ − 1) / r]

Where FV is your future value, P is your starting principal, r is the periodic interest rate (annual rate divided by compounding periods per year), n is the total number of periods, and PMT is your regular contribution per period.

A worked example

Notice how most of the final value comes from compounding, not from contributions. That's the magic. The catch: it requires time. Most of compounding's power happens in the final third of the investment period.

The Rule of 72

A handy mental shortcut: divide 72 by your annual rate of return to estimate how many years it takes for an investment to double. At 7%, money doubles roughly every 10.3 years. At 10%, every 7.2 years. At 4%, every 18 years. This works because of how exponential growth compresses time.

Things to consider before relying on a 7% return

• Returns are averages, not guarantees. The 7% number is a long-term historical average for diversified equities. Actual annual returns swing wildly — some years +25%, others −20%.
• Inflation eats into nominal returns. A 7% nominal return with 3% inflation is really only 4% in real (purchasing power) terms.
• Fees matter more than people think. A 1% annual fee may sound small, but over 30 years it can reduce your final balance by 20–25% due to lost compounding.
• Taxes apply outside retirement accounts. Capital gains, dividends, and interest are usually taxed when realised, lowering effective returns.
• Sequence of returns risk. Two portfolios with the same average return can end up with very different values depending on when the good and bad years fall.